Problem 14:Let A by M by N where M > N and consider the system of equations

(i) Ax = b where x is an N dimensional solution vector and b is an M dimensional vector of parameters.

Suppose the N columns ofA [A1,A2, . . ., AN] are linearly independent.

Under what conditions on b will a solution x to (i) exist and how could you compute it if it did exist?

Hint:Make use of the M by M elementary row matrix E which reduces A to upper triangular form U; i.e., E and U satisfy (28) and (29) in the picture below.